Set your Base Resolution to 1920x1080, and stretch your game video up. You won't be able to eliminate the bars, but that way you can either fill them with art assets, or slide the game to one side so both of the bars are on one side (just one big bar) that you can put a webcam or your Twitch chat inside, or fill with a wider art asset.
Alternately, you can force your monitor to run at 1600x900 and capture that. It will look weird and stretched for you, but your viewers will see it normally.
Otherwise, time to upgrade from a 16:10 aspect ratio monitor, to a more-standard 16:9 monitor.